Moir\'e dispersion of edge states in spin chains on superconductors

TL;DR

This paper investigates how moiré patterns influence the energy dispersion of edge states in ferromagnetic spin chains on superconductors, revealing ways to control and engineer these states for potential quantum applications.

Contribution

It introduces the concept of moiré dispersion in edge states and demonstrates how lattice modifications can control their energy behavior in spin chains on superconductors.

Findings

Moiré patterns cause energy oscillations in edge states.

Lattice modifications can control edge state dispersion.

Non-dispersive edge states can be engineered.

Abstract

Our calculations of ferromagnetic spin chains on s-wave superconductors show that the energy oscillations of edge states with the chain's length are due to a moir\'e pattern emerging from Friedel-like oscillations and the discreteness of the spin-chain lattice. By modifying the spin lattice, the moir\'e dispersion of edge states can be controlled. In particular, we can engineer non-dispersive edge states that remain at fixed energy regardless of the size distribution of the spin chains. This is an important step in the study of edge states of spin chains that can be fabricated with a certain size dispersion.